Virginia Beach, Virginia (CNN) -- The commando team that killed Osama bin Laden has already returned to American soil, a senior U.S. official said Wednesday. But in the town where they are widely believed to be based, you would never know it -- which is clearly by design.

While most soldiers returning from a war zone see an outpouring of welcome upon their return, in Virginia Beach, Virginia, it is quiet this week -- even though it is home to a storied team of Navy SEALs.

Virginia Beach Councilman Bill DeSteph is a former Naval intelligence officer, but he was mum when asked whether the American commandos who went to Pakistan are based here.

"No matter where these individuals are from," he said, "there's no city that will be able to confirm or deny, or throw a ticker-tape parade, or anything else."

SEAL Team Six is widely reported to operate out of Naval Air Station, Oceana, near Virginia Beach. The unit is covered with such a degree of secrecy that the military doesn't even acknowledge that it's here. And that code goes beyond operational security at the base.

Mayor Will Sessoms said, "you just want to reach out to them in some way, somehow, and say thank you." But the city, he told CNN affiliate WTKR, is honoring the servicemen's wishes. "They don't like the recognition, don't expect it, and it's a matter of keeping their families safe."

John McGuire, a SEAL for 10 years, says SEALs are not necessarily easy to spot, and do not have a stereotypical look.

"We're tall, short, large, not-so-large -- try to blend in and be Americans," he said.

Unlike most military personnel, SEAL team members do not necessarily maintain a telltale military-style haircut, since their missions sometimes require them to be inconspicuous.

At popular Virginia Beach eateries like Shuckers and Mary's diner, some patrons said they have a pretty good sense of who's who -- but only thanks to background knowledge that only a local would know.

"Maybe your next-door neighbor, you have an inkling of what he is," said Maryellen Baldwin, at the Navy League of Hampton Roads. "But we don't talk about them," she said.

At a popular nightclub, the manager said that if an altercation broke out, a SEAL would likely leave the scene quickly in order to avoid jeopardizing the anonymity that his job relies on. The club manager asked not to be identified so as not to alienate any military patrons by speaking publicly.

Even the spouses or girlfriends of SEAL team members are unlikely to know much about their work, according to Baldwin.

"That is part of the code, the code of silence," she said.

But even without knowing how to thank the people who killed Osama bin Laden, locals here express appreciation, and pride, over their work.

"We have the la creme de la creme in this area," said Leila Batman, the general manager at Mary's Restaurant.